Multi-party dialogue generation presents significant challenges due to the complex interplay of multiple speakers and interwoven conversational threads. Traditional approaches often fall short in capturing these complexities, particularly when relying on manually annotated dialogue relations. This paper introduces Speaker-Attentive LLM (SA-LLM), a novel generative model that leverages pre-trained Large Language Models (LLMs) and a speaker-aware contrastive learning strategy to address these challenges. SA-LLM incorporates a speaker-attributed input encoding and a contrastive learning objective to implicitly learn contextual coherence and speaker roles without explicit relation annotations. Extensive experiments on the Ubuntu IRC and Movie Dialogues datasets demonstrate that SA-LLM significantly outperforms state-of-the-art baselines in automatic and human evaluations, achieving superior performance in fluency, coherence, informativeness, and response diversity. Ablation studies and detailed error analyses further validate the effectiveness of the proposed speaker-attentive training approach, highlighting its robustness across different speaker roles and context lengths. The results underscore the potential of SA-LLM as a powerful and annotation-free solution for high-quality multi-party dialogue generation.